Space of modular forms of level 382, weight 2, and trivial character

• Label: 382.2.a
• Level: $382$
• Weight: $2$
• Character orbit: 382.a
• Rep. character: $\chi_{382}(1,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 382 = 2 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	382.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(382))\).

	Total	New	Old
Modular forms	50	15	35
Cusp forms	47	15	32
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(191\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(6\)
Minus space		\(-\)	\(9\)

Trace form

\( 15 q - q^{2} + 15 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{7} - q^{8} + 15 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(382))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	191
382.2.a.a	$382$	$2$	382.a	1.a	$1$	$3$	$3$	$3.050$	3.3.169.1	None	✓	$1$	$1$	\(-3\)	\(-1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
382.2.a.b	$382$	$2$	382.a	1.a	$1$	$3$	$3$	$3.050$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(3\)	\(-5\)	\(-6\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-2-\beta _{2})q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
382.2.a.c	$382$	$2$	382.a	1.a	$1$	$4$	$4$	$3.050$	4.4.6809.1	None	✓	$1$	$0$	\(4\)	\(3\)	\(4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{3})q^{3}+q^{4}+(1+\beta _{1})q^{5}+\cdots\)
382.2.a.d	$382$	$2$	382.a	1.a	$1$	$5$	$5$	$3.050$	5.5.176684.1	None	✓	$1$	$0$	\(-5\)	\(3\)	\(8\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(382))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(382)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 2}\)